I would not use a steel wire brush on the Villager side of the badge as it will remove base material from the badge (gouging ,scratching)
Use a brass brush for cleaning the badge but sometimes the brushes that are listed as brass are brass plated steel so check with a magnet if you have any doubts .
Brass wire is softer than steel wire or stainless steel wire, and offers a brushing action that will not scratch harder metals.Good for cleaning metal parts without removing any of the base material also good for Satin finishing aluminum extrusions or sheet.